bill them for your time. the morning of the exam is too late to be cancelling because of failing to secure accomodation. a motel doesn't suddenly become booked out - they obviousl;y hadn't booked themselves in. their failure. you had a contract with them to sit it on time/date, and they have failed to honour it, their notice being substantially deficient.
if you had an incident on the way to the exam and called and said that something that morning had prevented you from sitting said exam, you would fail it. why should they get away with it?